Articles

Cattaneo-Christov heat flux model for third-grade fluid flow towards exponentially stretching sheet

Expand
  • 1. Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000, Pakistan;
    2. Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000, Pakistan;
    3. Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan;
    4. NAAM Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received date: 2015-10-11

  Revised date: 2016-02-17

  Online published: 2016-06-01

Abstract

The Cattaneo-Christov heat flux in the two-dimensional (2D) flow of a third-grade fluid towards an exponentially stretching sheet is investigated. The energy equation is considered through thermal relaxation. Similarity transformations are accounted to obtain the ordinary differential systems. The converted non-dimensional equations are solved for the series solutions. The convergence analysis of the computed solutions is reported. The graphical results of the velocity and temperature profiles are plotted and elaborated in detail. The results show that the thermal relaxation enhances the temper-ature gradient while reduces the temperature profile.

Cite this article

S. A. SHEHZAD, F. M. ABBASI, T. HAYAT, B. AHMAD . Cattaneo-Christov heat flux model for third-grade fluid flow towards exponentially stretching sheet[J]. Applied Mathematics and Mechanics, 2016 , 37(6) : 761 -768 . DOI: 10.1007/s10483-016-2088-6

References

[1] Sahoo, B. and Poncet, S. Flow and heat transfer of a third-grade fluid past an exponentially stretching sheet with partial slip boundary condition. International Journal of Heat and Mass Transfer, 54, 5010-5019 (2011)
[2] Abbasbandy, S. and Hayat, T. On series solution for unsteady boundary layer equations in a special third-grade fluid. Communications in Nonlinear Science and Numerical Simulation, 16, 3140-3146 (2011)
[3] Hayat, T., Shehzad, S. A., Qasim, M., Asghar, S., and Alsaedi, A. Thermally stratified radiative flow of third-grade fluid over a stretching surface. Journal of Thermophysics and Heat Transfer, 28, 155-161 (2014)
[4] Hussain, T., Hayat, T., Shehzad, S. A., Alsaedi, A., and Chen, B. A model of solar radiation and Joule heating in flow of third-grade nanofluid. Zeitschrift fjr Naturforschung A, 70, 177-184 (2015)
[5] Sajid, M., Ahmad, M., Ahmad, I., Taj, M., and Abbasi, A. Axisymmetric stagnation-point flow of a third-grade fluid over a lubricated surface. Advances in Mechanical Engineering, 7, 1-8 (2015)
[6] Fourier, J. B. J. Théorie Analytique de la Chaleur, Chez Firmin Didot, Paris (1822)
[7] Cattaneo, C. Sulla conduzione del calore. Atti del Seminario Matematico e Fisico dell'Universit`a di Modena, 3, 83-101 (1948)
[8] Christov, C. I. On frame indifferent formulation of the Maxwell-Cattaneo model of finite-speed heat conduction. Mechanics Research Communications, 36, 481-486 (2009)
[9] Straughan, B. Porous convection with Cattaneo heat flux. International Journal of Heat and Mass Transfer, 53, 2808-2812 (2010)
[10] Straughan, B. Thermal convection with the Cattaneo-Christov model. International Journal of Heat and Mass Transfer, 53, 95-98 (2010)
[11] Tibullo, V. and Zampoli, V. A uniqueness result for the Cattaneo-Christov heat conduction model applied to incompressible fluids. Mechanics Research Communications, 38, 77-79 (2011)
[12] Haddad, S. A. M. Thermal instability in Brinkman porous media with Cattaneo-Christov heat flux. International Journal of Heat and Mass Transfer, 68, 659-668 (2014)
[13] Han, S., Zheng, L., Li, C., and Zhang, X. Coupled flow and heat transfer in viscoelastic fluid with Cattaneo-Christov heat flux model. Applied Mathematics Letters, 38, 87-93 (2014)
[14] Khan, J. A., Mustafa, M., Hayat, T., and Alsaedi, A. Numerical study of Cattaneo-Christov heat flux model for viscoelastic flow due to an exponentially stretching surface. PLoS One, 10, e0137363 (2015)
[15] Hayat, T., Imtiaz, M., Alsaedi, A., and Almezal, S. On Cattaneo-Christov heat flux in MHD flow of Oldroyd-B fluid with homogeneous-heterogeneous reactions. Journal of Magnetism and Magnetic Materials, 401, 296-303 (2016)
[16] Abbasi, F. M., Mustafa, M., Shehzad, S. A., Alhuthali, M. S., and Hayat, T. Analytical study of Cattaneo-Christov heat flux model for a boundary layer flow of Oldroyd-B fluid. Chinese Physics B, 25, 014701 (2016)
[17] Zheng, L., Wang, L., and Zhang, X. Analytic solutions of unsteady boundary flow and heat transfer on a permeable stretching sheet with non-uniform heat source/sink. Communications in Nonlinear Science and Numerical Simulation, 16, 731-740 (2011)
[18] Liao, S. J. Homotopy Analysis Method in Nonlinear Differential Equations, Higher Education Press, Beijng (2012)
[19] Turkyilmazoglu, M. Solution of the Thomas-Fermi equation with a convergent approach. Com-munications in Nonlinear Science and Numerical Simulation, 17, 4097-4103 (2012)
[20] Zheng, L., Zhang, C., Zhang, X., and Zhang, J. Flow and radiation heat transfer of a nanofluid over a stretching sheet with velocity slip and temperature jump in porous medium. Journal of Franklin Institute, 350, 990-1007 (2013)
[21] Abbasbandy, S., Hayat, T., Alsaedi, A., and Rashidi, M. M. Numerical and analytical solutions for Falkner-Skan flow of MHD Oldroyd-B fluid. International Journal of Numerical Methods for Heat and Fluid Flow, 24, 390-401 (2014)
[22] Hayat, T., Hussain, T., Shehzad, S. A., and Alsaedi, A. Flow of an Oldroyd-B fluid with nanopar-ticles and thermal radiation. Applied Mathematics and Mechanics (English Edition), 36, 69-80 (2015) DOI 10.1007/s10483-015-1896-9
[23] Shehzad, S. A., Hayat, T., Alsaedi, A., and Ahmad, B. Effects of thermophoresis and thermal radiation in mixed convection three-dimensional flow of Jeffrey fluid. Applied Mathematics and Mechanics (English Edition), 36, 655-668 (2015) DOI 10.1007/s10483-015-1935-7

Outlines

/

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals